The issue is not related to the shutter, or it’d affect all lenses. There’s a similar looking effect caused by too short a shutter exposure with flash, but that’s not what you’re experiencing here as you’re not using flash.

The problem is probably exacerbated by how you’ve mounted the lens to the camera, but it is also related to the lens itself. Some older lenses have heavy vignetting.

As can be seen here, vignetting is affected by aperture: https://m.dpreview.com/reviews/nikon-35-1p8g-n15/3

I believe your camera is crop-sensor? So likely what’s happening is that as you shut down the aperture the vignette is less blurred, and falls outside of the crop sensor.

I think Sony’s lens mount is fairly small which makes it harder to attach vintage lenses (compared to canon’s huge mount which allows non-optical adaptors for almost all lenses). If you’ve got an optical adaptor, that’s more likely to be causing a problem.

As for why it’s always on one side; this might mean you’ve got an inappropriate lens hood - take off the hood to check - or could be due to the lens design. However, it’s more likely related to your adaptor. Probably the adaptor hasn’t positioned the lens correctly.